Parallel Preconditioning of Large Sparse Systems of Linear Equations
Members of the project team
Research objectives
Large linear systems of linear equations cannot be solved using a
direct method because of memory and time constraints. Therefore
iterative methods are used for these problems. The convergence rate
of iterative methods can be improved dramatically by utilising a
so-called preconditioner: solving $M_1^{-1}AM_2^{-1}y = M_1^{-1}b$ and
calculating $x = M_2^{-1}y$ can be easier and less time-consuming then
solving the original system. Of course one must be able to calculate
$M_1^{-1}u$ and $M_2^{-1}u$ efficiently. Incomplete decompositions
are in many cases good preconditioners. Existing techniques to
increase the parallelism in the decomposition like multi-color
reordering and neglecting entries can have some success but usually
lead to a less efficient preconditioner.
Collaborations
Close collaboration with the Numerical Mathematics group of
prof. dr. H.A. van der Vorst at Utrecht University.
Intended results
New techniques are to be developed that increase the parallelism
in the decomposition and at the same time result in a preconditioner
that is equally efficient as the one obtained using the normal
sequential incomplete decomposition.
Recent publications
- A.C.N. van Duin and Harry A.G. Wijshoff,
ILU-preconditioning with a fill drop strategy based on strongly
connected components, techninal report, Department of Computer
Science, Leiden University.
Last modified on August 25, 1997 by Lex Wolters.